{
  "id": "math/0010128",
  "version": "v1",
  "published": "2000-10-12T19:18:57.000Z",
  "updated": "2000-10-12T19:18:57.000Z",
  "title": "Two characterizations of the standard unit vector basis of $l_1$",
  "authors": [
    "David Mitra"
  ],
  "comment": "Latex. 8 pgs",
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that for a sequence in a Banach space, the property of being stable under large perturbations characterizes the property of being equivalent to the unit vector basis of $l_1$. We show that a normalized unconditional basic sequence in $l_1$ that is semi-normalized in $l_\\infty$ is equivalent to the standard unit vector basis of~$l_1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-10-12T19:18:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B45",
      "46B15"
    ],
    "keywords": [
      "standard unit vector basis",
      "characterizations",
      "normalized unconditional basic sequence",
      "large perturbations characterizes",
      "banach space"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....10128M"
    }
  }
}